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COMPRESSED AIrW^Iv

ROBERT Z.\:INER, M.K.

NEW YORK:
D, VAN NOSTRAND. PUBLISBER,

23 MURBiT .BD S7 WiBREJ. StbU*.

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'_ CO

7 •-!

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PREFACE.

The subject of Compressed Air and
Compressed Air Machinery offers a wide
field for useful investigation. It has
been attempted in these pages to add
something to the scanty stoclt of its
hterature.

Compressed Air has become a most
elBcient and powerful agent in the hands
of the modem engineer. Its appHca-
cations are rapidly growing, both in
extent and importance. The subject
demands careful attention and study.

There can be no doubt that the great
waste of energy that to-day accompanies
the use of Compressed Air is due, not
only to sickly design and faulty -con-
Btruction of machines, but very largely
also to the general ignorance of the
principles of thermodynamics. Hence,
we have started with the general eqna-

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tioii of tl I ermo dynamics, which expresses
the relation between heat and mechani-
cal energy under all circumstances, and
have deduced from it ail the formulas
and results necessary to an intelligent
comprehension of our subject. We have
not tried to be simple by avoiding
the higher mathematical analysis; but
thorough and clear, by beginning at the
very bottom and fully explaining every
step and principle. It will not be neces-
sary for the average reader to study any
work on thermodynamics or higher
mittheraatics, preparatory to reading
this.

Zeuner's "Th^orie M6ehanique de la
Chaleur," Clausius, Rankine and McCuS-
loiigh on Heat, Riedler's " Luftcompress"
loiis-maschinen," have been freely used.
The works of MM. Cornet, Mallard and
Pochet and others, have all, I believe,
received credit in the text.

R. Z.

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TABLE OF CONTENTS.

1. Loss of Energy,

3. Methods of Cooling.

S. Conditions Most Favorable to the Highest
EfBciency.

4. Efficiency Attained in Practice.

5. Efficiency of Full Pressure and Complete

Eipanaion Compared.
S. Losses of Transmission.

Chaptbb II. — pHisicai. Propbiitibs ahd
Laws ok Air.

1. Introductory

2. Boyle's Law.

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8. Tlui Law o[ Gaj-Lussiic.

4. Boylo's and Gay-Lussac's Law.

5. Absolute Temperature.

6. The Law of Pi'essure, Deosity and Temper-

7. Tlie :*[ea3urement of Heat.

1. Iiitroductoiy.

3. Heat and Temperature.

3. The Two Laws of Therraodyn amies.

4. Heat and Mechanical Energy.

5. The Differential Equation of llie Second

I. The Determination of tlie Specific Heat at

Constant Volume.
%. Internal Heat,

3. Quantity of Heat Supplied.

4. Expansion with Temperature Constant.

5. Expansion in a Perfectly Non-Con due ting

Cylinder.

6. Variations in the Temperature of a Gas

during Aiiiabatic CompresBioa or Ex-

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1. Fundamental Formulas.

2. "Work Spent in Compression.

3. Work Obtainable from Compresaed Air.

4. The Theory of Compression.

5. The Theory of Transmission.

6. The Theory of Complete Expansive Work-

7. The Theory of Full Pressure Working.

8. The Theory of Incomplete Expansive

Working,

9. Graphical Represenlaliou for the Aclion of
Air.

1. The Efficiency of the Compressor and the
Compressed Air Engine as a Systera

3. Maximum Efficiency calculated from the
Indicated Work.

3. Efficiency of Full Pressure and Complete
Expansion Compared.

Chapter VII. — The Effects op Moisthrb,
OF THE Injection of Water akd ov

THE CONDUCTIOB OP IIEAT,

1. General Statement.
3. Effects of Moisture.
3. The Injection of Water.

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Chapter VIII- — Ambiucan and Europban

Allt COMI'KBHBORS.

1. Pump Compressors.

3. Single Acting Wet Compressors.

3. Double and Direct Acting Compressors.

i. Design and OoDstruction.

CiiAPTEK IX. — Examples pitoM Practick.

1. Republic Iron Company,

2. Economy Promoted by the use of Coni-

pressed Air.

3. Compressed Air Motor Street Cars.

Tadles. Page.

(. Values of _ -J, &c., for eonven-
rj V

ient values o." 72, 73

II. Pinal Temperatures of Compressed

Air 78

III. Final Temperature of after Espsii-

sion 84

IV. Theoretical Efficiencies 97

V. Tlieoretical Efllciencies for Full

Pressure and Complete Expansion. 100
VI. Effects of Moisture on final Temper-
ature 105

VII, Work of Isotliermal and Adiabatic-

Compression 108

VIIL Quantity of Water necessary iu

Compression 110

IX. Quantity of Water to bo Injected

into tiie Working Cylinder 113

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mmmm dF power by mmm m.

INTRODUCTION.
I.

HISTOKICAL NOTICE.

The application of compressed air to
industrial purpoaea dates from the close
of the laat century. Long before this,
indeed, we find isolated attempts made
to apply it in a variety of ways; but its
final success must be ascribed to the.
present age — the age of mechanic arts —
an age inaugurated in bo splendid a man-
ner by the genius of Watt, and which
has been so wonderfully productive in
good to mankind.

Without going into any details as to
its history, we shall only name the Eng-
lish engineers, Cubitt and B run ell,
who, in 1851-4, first applied compressed
air in its statical application to the sink-

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iiig of bridge caisaous; tlie (Jutioese Pro-
fessor, M. Collodon, who, in 1852, first
ooueeived and suggested the idea of em-
ploying it in tlio proposed tiinneling of
the Alps; and, finaliy, the distinguished-
French engineer, Sommeillei-, who fii'st
praoti^'aiiy realiKed and apjilied Collo-
don's idea in the bonng of the Mt. Cenis

riT, AFI'LICATIOXM A.VD IT.^ FL'IUKE.

Tlie applications of compressed air are
vijry numerous, its most imjiortant one
beuig the transmission of power by its
ineani<.

Custom has confined the term " trans-
mission of power " to such devices as are
employed to convey power from one place
to another, without including organized
machines through which it is directly ap-
plied to the performance of work.

Powei' is transmitted by means of
shafts, belts, friction- wheels, gearing,
wire-rope, and by water, ateam and air.
Tliere is nothing of equal importance

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connected with mechanical engineering
in regard to which there exists a greater
diversity of opinion, or in which there is
a greater diversity of practice, than in
the means of transmitting power. Yet
ill every case it may be assumed that
some particular plan is better than any
other, and that plan can be best determ-
ined by studying, first, the principles of
the different modes of transmission and
their adaptation to the special conditions
that exist; and, secondly, precedents and
examples.

For transmitting power to great dis-
tances, shafts, belts, friction -wheels and
gearing are clearly ont of the question.
The practical in compressibility and want
of elasticity of water, renders the hy-
draulic method unfit for transmitting
regularly a constant amount of powei'j
it can be used to advantage only where
motive power, acting continuously, is to
be accumulated and applied at intervals,
as for raising weights, operating punches,
compressive forging and other worlt of
an intermittent character, requiring a

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great force acting through a small dis-

Whether steam, air or wiro-rope is to
be made the means of transmitting power
from the prime-mover to the machine,
depends entirely upon the special condi-
tions of each case. In carrying steam to
great distances very impoitant losses
occur from condensation is the pipes;
especially during cold weather. The
wear and tear of cables lessen the ad-
vantages of the telodynamic transmis-
sion; steep inclinations and frequent
changes of dii-ection of the line of trans-
mission often exclude its adoption; while
it is entirely excluded when it is rather
a question of distributing a small force
over a large number of points than of
concentrating a large force at one or two
points.

Compi-essed air is the only general
mode of tvansmitting power; the only
one that is always and in every case pos-
sible, no malter how great the distance
nor how the power is to be distributetl
and applied. No doubt as a means of

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utilizing distant., yet hitherto unavailable,
sourcfiB of power, the importance of this
luedium can hardly be overestimated.

But compressed air is also a storer of
power, for we can accumulate any de-
sired pressure in a reservoir situated at
any distance from the source, and draw
upon this store of energy at any time;
which is not possible either in the case
of steam, water or wire-rope.

Larger supply-pipes are required for
steam or water transmission; the incon-
veniences resulting from hot steam pipes,
the leakages in water pipes, the higl
locitiea required in telodynamic trans-
mission are alt without their counter-
parts in compressed-air transmission.
Compressed air is furthermore independ-
ent of differences of level between the
source of power and its points of appli-
cation, and is perfectly applicable no
matter how winding and broken the j>ath
of transmission.

But especially is compressed air adapt-
ed to underground work. Steam is here
entirely excluded; for the confined char-

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acter of the situation and the difficulty
of providing sin adequate ventilation,
render its use impossible; compressed
air, besides being free from the objec-
tionable features of steam, possesses
properties that render its employment
conducive to coolness and purity in the
atmosphere into which it is exhausted.
The boring of such tunnels as the Mt.
Cenis and St. Gothard would have been
impossible without it. Its easy convey-
ance to any point of the underground
workings; its ready application at any
point; the improvement it produces in
the ventilating currents; the complete
absence of heat in the conducting pipes;
the ease with which it is distributed
when it is necessary to employ many
machines whose positions are daily
changing, such as hauling engines, coal-
eutting machines and portable rock-drills ;
these, and many other advantages, when
contrasted with steam under like condi-
tions, give compi-essed air a value which
the engineer will fully appreciate.

There is every reason to belicviL' litat

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compressed air is to receive a still move
extensive applioation. The diminished
coat of motive power when generated on
a large scale, when compared with that
of a number of separate steam engines
and boilers distributed over manufactur-
ing districts, and the expense and danger
of maintaining an independent steam
power for each separate establishment
where power ia used, are strong reasons
for generating and diatvibuting com-
pressed air through mains and pipes laid
below the surface of streets in the same
way as gas and water are now supplied.
Especially in large cities wOuld the
benefits of such a, system be invaluable;
no more disastrous boiler explosions in
shops filled with hundreds of working
men and women;, the danger of fire
greatly reduced; a corresponding i-edue-
tion in insurance rates; an important
saving of space; cleanliness, convenience
and economy. We say economy ! For
there is no doubt that a permanently
located air-compressing plant, established
on a large acale, and designed on princi-

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plee of true economy and not witli refer-
ence to cheapness of construction, would
supply power at a much less cost than is
supposed. Besides, there are many natu-
ral sources of power, as water power,
which could by this means be utilizL'd,
and their immense stores of energy con-
veyed to the great centers of business
and manufacture.

As affording a means of dispensing
with animal power on our street rail-
roads, compressed air has been proposed
as the motor to drive our street cars. It
has already mot with some success in this
direction, and, to-day, there are eminent
French, English and American engineers
at work upon this interesting problem.

The compressed-air locomotives of M.
Ribourt, now in use at the St. Gothard
Tunnel, give very satisfactory results,
Tliey are compact, neal and compara-
tively economical.

Compressed air is also applied in a va-
riety of other ways; in signaling, in pro-
pelling torpedo boats; in ventilating
iarge and confined spaces; in driving

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machinery in confined shops; in sinking
bridge caiasODs. The pneumatic dis-
patch system, the air brake, th^ pneu-
matic elevator and hoist, are further ex-
amples of ita use.

CHAPTER I.

The Conditions Modifying Efficiency

IN THE Use op Compressed Air.

LOSS OF ENERGY.

What is at present required in the use
of ".lompressed air is a considerable dim-
inution in the first cost of obtaining it
by really improving the compressor, and
a practical means of working it at a high
rate of expansion without the present
attendant losses. In the best machines
in use at the present day, the useful ef-
fect, that is, the ratio of the work done
by the air to that done upon it, is very
small. The losses are chiefly due to the
following causes;

1. The compression of air develops
heat; and as the compressed air always

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cools down to the temperature of the
surrounding atmosphere before it is
used, the mochauical equivalent of this
dissipated heat is work lost.

2. The heat of compression increases
the volume of the air, and hence it is
necessary to carry the air to a higher
pressure in the compressor in order that
we may finally have a given volume of
air at a given pressure, and at the tem-
perature of the surrounding atmosphere.
The work spent in effecting this exuess
of pressure is work lost,

3. The great cold which results
when air expands against a resistance,
forbids expansive working, which is
equivalent to saying, forbids the realiza-
tion of a high degree of efficiency in the
use of compressed air.

4, Friction of the air in the pipes,
leakage, dead spaces, the resistance of-
fered by the valves, insnificiency of
valve -area, inferior workmanship and
slovenly attendance, are all more or less
serious causes of loss of power.

The question now is, how can we get

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rid of these losses and obtain n highei

The first cause of loss of work, name-
ly, the heat developed by compression,
ia entirely unavoidable. The whole of
the mechanical energy which the com-
pressor-piston spends upon the air is con-
verted into heat. This heat is dissipated
by con d notion and radiation, aniJ its me-
chanical equivalent ia work lost. The
compressed air, having again reached
thermal equilibrium with the surrownd-
ing atmosphere, expands and does work
in virtue of its inti-insic enefcgy.

We proceed to the second loss, which
is the work done in driving the com-
preaaor-piston against the increase of
pressure dae to the heat of compression.
Since the temperature increases more
rapidly than it ought, according to
Boyle's law, the work necessary to com-
pression is greater than if the tempera-
ture were to remain constant.

The theoretical efficiency of the com-
pressing and working cylinders, as given
further on by eq. {*80), is:

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where r^ is t!ie absolute temperature of
the air at its exit from the compressor,
and 6, the absolute temperature at its
entrance into the working cylinder, which
in practice is that of the surronnding
atinoapherc. Hence we can increase the
value of this fraction only by decreasing
the denominator r„ that is the final heat
of compression. This can only be done
by .abstracting the heat during compres-
sion, or by using very low pressures.
But low pressures are excluded by other
considerations. Tlie weight of air, w,
needed per second to perform a given
amount of work would liave to be con-
siderably increased, and this would neces-
sitate larger pipes, larger cylinders, and
would result in a cumbrous and espen-

The only remaining alternative, there-
fore, is to bring about in the compressor
tlie cooling which the air now under-
goes after having left it. Table VII
^hows respectively tlie ]>ortion of work

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lost when the air is not cooled in the
compressor and that lost when it is com-
pletely cooled, and will make manifest
the advantage there is in cooling. For
a pressure of six atmospheres the work
spent in isothermal compression to that
spent in adiabatic compression is as 3 to
4; and this ratio decreases rapidly as the
pressure increases.

II.

MET[[ODS OF COOLING.

There ai-e three methods in which cold
water is applied to cool the air during
its compression:

1. In case of the so-called hydraulic
piston or plunger compressors, the air is
over and in contact with a column of
water which acts upon the air like an
ordinary piston, its sui-face rising and
failing with the backward and forward
motion of the plunger. It is obvious
that the cooling effect of this large mass
of water is very small. There is nothing
but surface contact, and water possesses
in a slight degree only, the property of

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-22

conducting, through its mass, heat re-
ceived on its surface. But we obtain all
the advantages there are in having the
air completely saturated with water-
vapor during its compression, as well as
all the disadvantages of having saturated
compressed air to work with. What has
been here said of hydraulic plunger-
compressors, applies equally to hydraulic
or i-am compressors (first used by Som-
meiller at Mt. t'enis, but now obsolete).

2. By flooding the external of the
cylinder, and sometimes also the piston
and piston-rod. This method of cooling
presents neither the advantages nor dis-
.idvantages incident to direct intereon-
tact between the air and water; it is that
generally adopted in American practice,
especially where it is necessary to expose
the air-pipes to the out-door atmosphere
of winter. The cooling which it effects
is, however, only an approach to that
which insures the highest efficiency.

3. By injecting into the compressor-
cylinder a certain quantity of water in a
state of the finest possible division, .'. v., in

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the form of spray. This method of cooling
was first applied by Prof. Collodon in the
compresBora used at the St. Gothard
TuEnel. It is by fai' the most rational,
complete and effective. In this fine state
of division the water has many more
points of contact with the air, which is
both completely cooled and kept thor-
oughly saturated during compression. It
is extremely important that the quantity
of water injected into the compressor
be a minimum, and hence the weight I'e-
quired for different tensions is given in
a table further on.

III.

COHDITIONS MOST FAVORABLE TO ECONOMY
IN THE USE OF COMPRESSED AIR.

By working air at full pressure we
avoid the formation of ice in the pipes
and exhaust poits, not so mnch because
the air is less cooled (for the great fall
of temperature produced by the sudden
expansion at the instant of exhaust is
almost equal to that produced by inte-
rior expansion), but because the air in

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exhaasting acquires a high velocity, and
this opposes the deposit of ice crystals
by its purely raechauical effect, and by
the heat developed by its friction.

But even at full pressure we cannot
work with bigli tensions without serious
drawbacks. lit Kngland, several trials
were made at the Govan Iron Works and
other places to use air under tensions of
eight and nine atmospheres, but tbey
were forced to return to low pressures,
owing to the entire an-est of the ma-
chine from the formation of ice in the
ports. Hence, not taking into account
the fact that the useful effect decreases
as the pressure increases, we conclude
that it is not good practice, even at full
])re8snre, to work with a tension much
over four atmospheres, unless we employ
special means to reheat the working air.

But while by working at full pressure
with moderate tensions, we avoid the in-
conveniences of veiy low temperatures,
the eificiency obtained is also very iow.
Notwithstanding this, even up to the
present time air ia almost exclusively

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worked at full pressure, especially in the
United States. This is because the great
cold produced by expansive working has
made its adoption impossible. With a
cut-off at i stroke the temperature of the
air falls 71° C, and at | cut-off 140° C.

Now, to avoid these low temperatures,
it is necessary either that the initial tem-
perature of the compressed air be raised
by heating it before its introduction into
the working cylinder, or that the cylin-
der in which it expands be heated, or
that the compressed air be supplied with
heat directly during its expansion by
means of the injection of hot water.

In 1860, M. Sommeiller, in order to
utilize expansion, heated his working
cylinders at Bardonnfiche by means of a
current of hot air circulating around the
cylinders in small pipes. By this means
he was enabled to cut off at |- stroke.

In 1863, M. Devillea recommended
that the cylinder be placed in a tank
through which hot water was to circu-
late. Other devices were to place the
cylinder into a tank of water, into which

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from time to time fresh supplies of quick-
lime were to be thrown. Waste cotton,
soaked in petroleum, was also used to
beat the working cylinder.

Finally, in 1874, Mr. C. W. Siemens
proposed the injection of hot water into
ihe compressed air engine cylinder to
keep the temperature of the expanding
air from falling below the freezing point,
just as wo inject cold water into the
compressor cylinder to prevent a great
rise of temperature dining compression.
This is by far the most efficient mode of
supplying heat to the e;;panding air. Ex-
pansion is made completely practicable,
and hence the efficiency of the engine ia
greatly incj-eased, as was shown by M.
Comet, who was the first to apply Mr.
Siemens' plan and to prove conclusively
its great practical utility.

The quantities of hot water to he in-
jected into the cylinder should always be
a minimum; they are given In a table
further on.

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IV.

EFFICIENCY AITAINED Itl TRACTICE.

It is desirable to know what efficiencies
have been attained in practice — ^of com-
pressors, of compressed -air engines, and
of the two machines together as a
system.

1. By efficiency of compressor is meant
the ratio of the efEective work spent upon
the air in the compressor to that de-
veloped by the steam in the driving en"
gine; or if you choose, the resistance di-
vided by the power.

a. In compressors without piston or
plunger, such as the hydraulic com-
pressor of Sommeiller, the efficiency is
always less than .50. These machines
are interesting on account of their sim-
plicity, bnt their useful effect is always
vei-y small,

6. In the so-called hydraulic piston
or plunger compressor, an efficiency of
,90 has been obtained when working at a
low piston-speed to pressures of faur and
five atmospheres.

c. The compressors of Albei-t Schacht

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at Saarbriicken, in which llie cooling is
wholly external, have sliowii an efQciency
of ,80 when compressing to a tension of
4 effective atmospheres.

'I. Prof. Collodon's eompvessors, into
which water is injected in the fonn of
spray, and which were run at a piston-
speed of 345 feet, and compressed the
air to an absolute tension of 8 atmos-
pheres, gave an efficiency which never
descended below .80, while the tempera-
ture of the air never rose higher than
from 12 to 15 degrees C.

'.'. The efticiency of compressed-air
engines is the ratio of the work which
they actually do, to that which is theo-
retically obtainable from the compressed
air. The following are examples of its
value as found by experiment:

At the Haigh Colliery, Eng., .70
" " Kyliope " " .66

M. Eibourt has found for his locomotives
.50 to .60.

In general it may be said that in the
very best machines we can count upon
from .To to ."75; while in the ordinary

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ones, working against a variable resist-
ance, this eliiciency descends to .50 and
.55.

3. The efficiency of the whole system
together, that is, the ratio of the work
measured on the crank-shaft of the com-
pressed-air engine, to that done by the
prime mover, is found to be about .2() to
.25 for high pressures, and from .35 to
.40 for low pressures.

Experiments made at Leeds show a
net efficiency of .2S5 when working with
2,75 effective atmospheres, and .455 when
with 1.33 atmospheres.

At the Blanzy mines, M. Graitiot has
found for a final efficiency, .22 to .32 of
the effective work of the steam.

M. Ribourt, by experimenting on the
new compressed-air locomotives built
for the St. Gothard Tunnel, found that
the ratio of the tractive effort developed
to the original power, {in this case a
head of water), was .23; that is, after
passing the turbine, the compressor, the
expansion regulator, and the cylinders of
the locomotive, there remained .23 of
the original power.

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•IF i:Xl'ANMlllX <^OMrAREU,

Let W, b(! the work sjienl upon llic aif
in tlio compressor;

W, the work which the compressed air
is theoretically able to do; then its the-

W
orelieal efficiency will be ^-.

If W=the actual work doiiL' l)y liif
prime mover, and

W the actual work done i;y the air,

llieii llie real efficiency will be ^ .

Kow in tliL' ordinary conditions of
practice we know that W, is at best .Tu
W", and W is only about .70 W,; hence

, ^ ■ vv .row W

t =rea! eftcieiicy=^.- =-^--■ = ^.49---

Tto"" -.4UK.
W
Tlic value of ^' {=E=the theoretical

efficiency) is .55 for full presHure and
.75 for complete expansion. Hence, suli-
stitiiting these values of E above, wi-

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find for these twn cases a final efficiency
of .27 and .37.

VI.

LOSSES OF 1

The losses due to transmission are cal-
culated further on.

At the ■works for excavating the Mt.
Cenis Tunnel, the supply of compressed
air was conveyed in cast iron pipes 1^
inches in diameter. The loss of pressure
and leakage of air, from the supply pipes,
ill a length of one mile an<i flfleen yards,
was only 3^^ of the head; the absolute
initial pressure was 5.70 atmospheres,
and it was reduced to 5.50 atmospheres
whilst there was an expenditure at the
rale of 64 cubic feet of compressed air
per minute. In the middle of the tun-
nel, through a length of pipe of 3.8 miles,
the absolute pressure fell only from six
atmospheres to 5.7 atmospheres, or to ,95
of the original pressure.

At the Hoosac Tunnel the air was car-
ried through an 8-inch pipe from the
compressors to the heading, a distance of

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7,150 feet, operating six drills', wilh an
average loss of tvn pounds pressure.

CHAPTER II.

The PiiYsic-Ai. Pe<iperties avd Law:?

OF AlK.

INTliOnUCTOKY.

A fluid is « body incapable of resisting
a change of shape. Fluids are either
liquids, vapors or gasea. Water may be
taken as the type of the first; steam is
the type of all vapors, and air of all
gases.

Gases are either coercible gases, i. e.,
such as under ordinary circumstances
may be condensed into liquids or even
solids, as CO,; or permanent gases, which
retain their aeriform stale under all ordi-
nary circumstances of temperature and
pressure. This distinction is convenient.
Air has been condensed, bnt certainly
not undei' ordinary circumstances.

Air then is a permanent gas, and may
be considered 2, per feat fluid ; that is,

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1. It is incapable of experienising a
distorting or tangential stress, its mole-
cules offering no resistance to relative
displacement among themselves; lienee
no internal work of displacement need
be considered.

2. It has the power of indefinite expan-
sion 80 as to fill any veBsel of whatever
shape or size.

3. It exerts an equal pressure upon
every point of the walls of the vessel
enclosing it.

4. It is of the same density at every
point of the apace it occupies,

II.

liOYLE'S LiW.

This law states that the temperuturt
being constant, the volume of a gas varies
inversely as the pressure / formulated:

pv'=p„v, (1)

Where u^^the volume of a given
weight of the gas at freezing tempera-
ture and a pressure p^; and u'^lhe vol-
ume of the same weight of gas at the
same temperature and at any pressure p.

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IJry air, a mecbaiiical niixlui
oxygen and nitrogen, being a pei
gas, obeys this law.

III.

This second law of ganey may In'
stated thus: Jhe volume of u gas undet
constant pressure ea^ands loJten raisit/
Ji-om the freezing to the boihng tcmjm -
atare, by the same- fraction of if^elf,
whatever be the natttre oft/ie gai , form
ulaled :

it lias been found by the careful
experitnents of MM. Rudberg, Reg-
nault and Prof. Balfour Stewart and
others, that the volume of air at constant
pressure expands from 1 to 1.3665 be-
tween (i° 0. and 100"^ C. Hence for a
variation in temperature of 1° C, the
volume varies by .003665 or g|>[- of thi.'
volume which the air occupied at 0°(,'.
and under the assumed constant pressure.
In equation (2) the coeiRcient a, is there-
fore equal to v\^.

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IV.

botle's and oay-i.ussac'b law.
Combining tlie equation formulating
Boyle'a law with that formulating Gay-
Lussac's, we obtain,

or letting «=— = 273, we have

pv=X& (<, + ,)=E (« + () (8)

This last equation is a general expres-
sion for both Boyle's and Gay-Lusaac's
law, and completely expresses the rela-
tion between temperature, volume, and
pressure.

K ia a constant and depends upon the
density of the gas. Its value for at-
mospheric air is determined as follows:

The weight of the standard unit of
volume of a substance in any condition
is the specific weight of that substance in
that condition.

The apeeijic weight of air, that is t
say, the weight of a cubic foot of air at

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0"C. and under a pressure of 29.92 inches
of mercury, is, according to M. Eegnault,
.080728 lbs. avoirdupois.

The specific vobime of a gas is the vol-
ume of unit of weight; it is the recipro-
cal of the specific weight.

Tlie specific volume of air, i.e., the vol-
ume in cubic feet of one pound avoirdu-
pois at 0° C. and under the pressure of
29.92 inches mercury is:

v^=~ — -— =12,387 cubic feet.
" .080728

Let /),=2116.4, the mean atmospheric

pressure in lbs. per square foot. Then

,, »„v„ 2116.4X12,387

ABSOLUTE TEMrERATUKE.

Making i= —273 in the equation
})v=R(<' + t\
tile second member reduces to zero, and
hence.

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The distance of the freezing point
from the bottom of the tube of an air
thermometer is to the distance of the
boiling point from the bottom as I ; 1.3665.
Hence, in the centigrade scale, where
the freezing point is marked 0° and the
boiling point 100°, the bottom of the
tube will be marked— 2 7 2". 85. The
lowest reading of the scale is, therefore,
— 273°, If this reading could be ob-
served it would imply that the volume
of the air had been reduced to nothing.
This is evidently a purely theoretical
conception; hut in dealing with questions
relating to gases it is exceedingly con-
venient to reckon temperatni-es, not from
the freezing point, but from the bottom
of the tube of an air thermometer. Ab-
solute zero, therefore, is marked— 273° on
the Centrigrade scale (con'esponding to
— 459. °4 on Fahranheit's scale), and is
the temperature at which all molecular
motions cease, and the mechanical effect,
which we call pressure, and which is due
to these motions, becomes zero.

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LAW 111'- THE PEESSUKE, DENSITY AXD
TBMI'EKATUBE.

Let D^=tlie density of a weight "■ of
air at the temperature 0' C. and under
the pressure jo^, i\ being the con-espoiid-
ing volume;

D=ita density at pressure/), tempera-
ture ?, V being its corresponding volume;

D'=its density at temperature 0° C.
pressure p and volume t'.

We shall have

or by taking ?'■ canity,

D4,„d.=i-.

Placing these values of v'

' and i\ i

equation (1), we get

r,_Ty,
l: D.'

that is, th6 pressure of a gus

is propo'i

tional to its density.

From (2) we have,

D_ 1 _ a

D' !+«'; r( + i'

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That is, the density of a gas is inversely
as its temperature, the latter being rec-
oned from absolute zero.

Combining equations (4) and (5),
D H a

P=^ X

-D.

But D= — , and hence

,<«+')„

(«)

lo)

(6) shows that the density of a gas is:
At constant tetnperature, directly as the

pressure ;

jit constant pressure, inversely as the

absolute temperature.

^=conetant for any given gas. For

to Rankine, 26214); this is the height in
feet of a column of fluid of density D„
which produces a pressure p^ pounds per

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square foot of surface; letting H be this
height, the weight of the column having
one square foot for its surface will be
D,n, or

D.H=/)..
If in (Of/) we make v=], we get

axt ^R

which is the weight of uDit of volume,
or the specific weight of air.

Making M=l in same equation, we
have for the volume of unit of weight,

X- =lt-

(s)

called the specific vilinne.
are reciprocals of each othei

THE MEASUREMENT OF HEAT.

Any effect of heat may be used as a
means of measuring it, and the quantity
of heat required to produce a particular
effect is called a thermal unit. It has
been found best to take a thermal unit to
be the quantity of heat wliich corre-

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sponds to some definite interval of tem-
perature in a definite weight of a
particular substance,

Def. A Briiuh Theiinal Unit is the
quantity of heat which corresponds to an
interval of one degree of Fahrenheit's
scale, in the temperature of one pound
of pure liquid water at its temperature
of greatest density (39°.l Fahr).

Def. A Calorie, or French Thermal
Unit, is the quantity of heat which
corresponds to the Centigrade degree in
the temperature of one kilogram of pure
liquid water, at its temperature of great-
est density, (3°.94 C).

Def. The Recife Seal of a body, is
the ratio of the quantity of heat required
to raise that body one degree, to the
quantity required to raise an equal
weight of water one degree.

It has been proven for permanent
gases, that,

1. The specific heat is constant for
any given gas, and is independent of the
temperature and pressure;

2. The thermal capacity per unit of

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volutin?, is the same for all eimple gases
when at the same pressure and tempera-
ture;

U. The specific heat increases with the
temperature, and probably with the
pressure, when the gas is brought near
the point of liquifaction, and ao longer
obeys Boyle's law.

The above three conclusions are true
of specific heat at constant vohime, as
well as of specific heat at constant jyixss-
ure, as far as regards simple gases and
air, (which, being a mechanical mixture,
obeys the sanaie laws as a simple gas).

It was shown by Laplace, that the
specific heat of a gas is different, accord-
ing as it is maintained at a constant
volume, or at a con^taat pressure, during
the operation of changing its tempera-
ture.

The specific lieat of gases was inde-
pendently determined by M. Regnault
and Prof. Rankine; experimentally by
the former, and theoretically by the
latter. Their results agreed exactly,
and are those now generally accepted.

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As given in Watt's Dictionary of Cliem-

Tlie specific heat at constant pressure
is .238.

As we shall find farther on, the specif-
ic heat at constant volume is .169.

CHAPTER III.

THERjiom-sAiiic Prisciples and For-
mulas.
I

INTKODUOTORT.

It is well known that the cylinder of
an air compressor becomea very hot even
at a low piston- speed. This fact brings
us face to face with the doctrine of the
conversion of energy; for it is the con-
version of the visible, mechanical energy
of the piston into that other invisible
form of energy called heat. Thus we
see we are at the very outset confronted
with a thermal phenomenon, whose con-
sideration involves the science called

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thermody mimics. To begin wiUi we
had no other but the visible meohanical
energy of a moving piston; but very
soon sensible heat manifests itself, anil
this heat can be developed only at the
expense of part at least, of the energy of
the moving piston.

These phenomena are referable to the
two genera! principles which form the
basis of the science of thermodynamics,

1. All forms of energy are convertible.

2. The total energy of a substance or
system cannot be altered by the mutiial
actions of its parts.

"The conversion of one foi-m of
energy into another takes place with as
gi-eat certainty and absence of waste,
and with the same integrity of the ele-
mentary magnitude, as the more formal
conversion of foot-pounds in kilogram-
meters." " In the development of the
axioms that nothing ia by natural means
creatable from nothing, and that things
are equal to the same thing only which
are equal to each other, and in the appli-

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cation to them of empirical laws with
reference to the behavior of bodies under
the action of heat and mechanical effect"*
consists chiefly the science of thermody-

The general equation of thermody-
mamics which expresses the relation be-
tween heat and mechanical energy under
all circumstances, was arrived at inde-
pendently, in 1849, by Professors Clati-
sius and Rankine. The consequences of
that equation have since heen developed
and applied by many distinguished
writers.

Of course we shall here confine onr-
selves to so much only of the JUechanical
Theory of Heat as is necessary to an in-

lligeiit comprehension of oiir subject;
and, in doing so, shall follow in outline
treatment given byM, Poehet, in bis
admirable "JVouvelle M^haniqiie Indus-
'ridle" making free use, at the same
Ime, of the works of Zeuner, Rankine
Clausius'.

ory of Dyniain

cal Tlieoty at Ifettl,""by "lUe

r Poldler, M.B.

in PopidiT Soie-ice Monthly

ry, ISIS.

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HEAT AND TGiirEEATUBE.

Heat denotes a motion of particles on
a sraall scal^ just as the rushing together
of a stone and the earth denotes a mo-
tion on a large scale, a mass motion. It
is dae to a vibratory motion impressed
upon the molecnles of a body. The
more rapid the vibrations the more in-
tense the heat. The quantity of heat in
a substance could be measured by multi-
plying the kinetic energy of agitation of
a single molecule by the number of mole-
cules in unity of weight, supposing the
substance to be homogeneous and the
heat uniformly distiihuted. Thus the
thermometer and dynamometer reveal to
us phenomena which are in reality ident-
ical, and we can estahlit^li a measuring
unit to which both effects can be referred.

Temperature is the property of a body
considered with reference to its power of
beating other bodies. It is a function of
the variables, volume and pressure, or.

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that is, all bodies hamng the same press-
ure and volume have the same tempera-
ture. This \a expressed by the differen-
tial equation:

where 1-^-1 and I -^1 are the partial dif-
ferential co-efficientB;rf( in theformer de-
noting the increment of ; when, v re-
maining constant,^ alone is increased by
dp ; and in the latter, the increment re-
ceived by ( when p remaining constant,
V is increased by dv ; whilst in the first
member of the equation, dt represents
the total increment of i due to the simul-
taneous reception by p and v of the in-
crements dp and dv, respectively.

III.

THE TWO LAWS OF THBKMO DYNAMICS.

The whole mechanical theory of heat
rests on two fundamental theorems: *
1. That of the equivalence of heat and

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work; whensoever a body changes its
state in pi-odudng exterior work, (posi-
tive or negative), there is an abaoi-ption
or di sen gage meEt of lieat in tlie propor-
tion of one British thermal unit for every
772 foot pounds of work, (or of one
French thermal nnit for every 4l>3.55
kilogr ammeters of work).

This medianical equivalent of heat
was first exactly determined by Mr.
Joule, in honor of whom it is called
Joule's equivalent, and is denoteil by the
symbol J,

2. The theorem of the eqnimtleta-t of
traiisfurmatioiis; when a body is sutjcess-
ivi'ly put in communication with two
sources of heat, one at a higher tempera-
ture t, the other at a lower temperature
(„, its lempei-atui-e remaining constant
and equal to that of each source during
the whole time of contact, and the body
neither I'ecelving nor losing heat except
by reason of its contact with the two
sources, the ratio of the quantity of heat
Q given out by the higher source to the
quantity Q' transferred to the lower

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source, is independent of the nature of
the bodies; it dependa only on the
temperatures, ( and („, of the. two
souroea,

Clausius states this as follows: In all
cases where a quantity of heat is con-
verted into work, and where the body
effecting this transformation ultimately
returns to its original condition, another
quantity of heat must necessarily be
transfoi-red from a warmer to a colder
body; and the magnitude of the last
quantity of boat, in relation to the fireti
depends only on the temperature of the
bodies between which heat passes, and
not upon the nature of the body effecting
this transformation ; or, more briefly,
heat cannot of iUelf pass from a colder
to a warmer body.

IV.

HEAT AND MECHANICAL ENERGY.

The quantity of heat which must be
imparted to a body during its passage,
in a given manner, from one condition to
another, (any heat withdrawn from the

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body being counted an important nega-
tive quantity) may be divided into three
parts, viz r

1. That employed in increasing the
heat actually existing in the body;

2. That employed in producing in-
terior work.

3. That employed in producing ex-
terior work.

The first and second parts, called I'e-
spectively the thermal and ergonal con-
tent* of the body, are independent of
the path pursued in the passage of tbe
body from one state to another; hence
both parts may be represented by one
f auction, which we know to be com-
pletely determined by the initial and
final states of the body. The third pai-t,
the equivalent of exterior work, can oidy
be determined when the precise manner
in which the changes of condition took
place is known.

Let rfQ=the element of heat absorbed
during an infinitesimal change of con-
dition;

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U„=the free heat present in the body
at the beginning, i.e., the body's intrinsic
energy;

U=the free heat present in the body
at the end of the change, plus the heat
consumed by internal work during the
change of state;

pdv will be the work accompanying
the passage of the body from a state
(p, v) to a state {p + dp, v + dv);

Then the heat spent while the body
passes from one temperature t to another
t + de, and from one state {p,") to an-
other (p+dp, v + dv) will be :

dq=cu--u,) + \.pdv,

(10)

where dU depends upon the in.
^nal circumstances, while y.^ifu

on the intermediate circumstances of the
change of state.

We can write d\J=o and entirely ex-
clude interior work and heat by confining

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ourselves to cyclical ■pi'oce.^ses, lliat is to
say, to opevations in which tlie modifica-
tione which the body undergoes are so
arranged that the body finaily returns
exactly to its original condition, the inte-
rior work, (lositive and negative, exactly
neutrfiliziiig each other.

that ia, the internal iieat of a body de-
pends only upon the volume of the body,
and the pressure to which it is subjected.
Hence the increase of internal heat when
the body passes from a state (y), v) to a
state (p-^-dp, v-^dv) will be:

Substituting in equation (10) the value
of (H^T as given by equation (11), we have

an equation which is not integrable ;
since this would require that the second
derivatives of the co-efticients of dp and

dv (which are, respectively, ^-- and

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other*; this would imply the impossible
condition J— o. That is, mechanically
speaking, the quantity of heat passing
cannot be expressed as a function of the
initial values of p and v. The equation
can only be integrated when we have a
relation given, by means of which t may
be expressed as a function of v, and
therefore p as a function of v alone. It
is this relation which defines the manner
in which the changes of condition take
place; the quantity of heat passing de-
pends upon the intermediate circum-
stances of change of state, circumstances
which may be anything.

When a body is heated from a tem-
perature ; to another t-{-dt, preserving
the same volunie, no external work will
be done and do=o. Hence eq. (12) will
become:

=c^ dt (13)

1. 366; aJeoMcCul-

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(1,S«)

which, by definition, is the specific heat
at co)tsti.int volume.

The abovG eqnation gives:

it,. '\i,,}

the partial differential eo-efiicient of (
with reapect to p.

If the body passes from t to t + dt
under coiistant pressure, d//—o, and henee
(12) becomes:

which, by definition, is the apecijic keut
at conaUint pressure.
From (U) we have:

("«)

Substituting these values of the partial
derivatives iti eq. (l'2), we obtain a sec-
ond expression for t^Q, viz. : '

"«=».(!)*+

It is convenient to liave this equation
n a form involving only the temperature

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and specific heats, and not the quantity
Q. We obtain such a form by difEeren-
tiating (13a) with respect to w, and (14«)
with respect to p and subtracting the
first result from the second. The form
obtained is:

= (c-c,)

dt\

l\<lpl
(16)

STIAL EQCATiON ■
SECOND PRIXCIPLE.

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6f;

1. Let OA=ttie initial volume of a
body whose temperature is ( y it expands
ill contact with a source of heat, (isother-
mally), from volume OA to volume OB,
when its temperature is then still (.

Q=the quantity of heat supplied by
tlie source.

2. It is now left to expand adiabati-
cally, i.e.. without the addition or sub-
traction of heat, from volume OB to
Tolume OC, when its temperature will
have fallen to t^.

3. Now place it in contact with a
source of heat of the same tern [jeiature
;„, and compress it from OC to OD,
when ilB temperature is still t^.

Q'=:the quantity of beat tliat has
passed into the source.

4. Compress it adiabatioally from
volume OD to volume OA, when its
temperature will again be (/ the body
has now undergone a complete cycle,
during which it has evidently done wort
represented the area abed ; hence,

Q— Q'=beat disappeared, and from
the first law of tbermodynaraies,

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Q~Q,= 1 Xa6c(7= J xA. (lY)

Now the second law of thermodynam-
ics states that Q and Q', (the heat
received and the heat given out), are
independent of the nature of the bodies,
and dependent only upon the tempera-
ture.

Suppose that the differeuce of temper-
ature of the two sources of heat is
infinitely small, ( and l + dt. Also
consider t and v as the independent vari-
ables determining the state of the body,

?=/(«, <)■

A, in the above equation, is the in-
tegral between n, and v of the elementary
areas, such as ef. Now if Ke=p, E/is
what p will become when the volume
remains constant, and the temperature
takes an increment dt ; fe therefore
measures the differential increment

where -^=the partial derivative of p
with respect to t.

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■'3-«'='*-3=j/'

i't

\dtdv

v:.(i)'

taking the inclependent variable dt out
of the integration symbol.

Q is the beat auppliecl to keep at t the
temperature of the body expanding
from u„ to v; and, therefore,
Q=*((,'j„,)j/ the nature of the bodies);
also,

Q'=F"((, i'„M)=F((),
the variables y^, v being implicitly con-
tained in F.

Since Q=Q' when ( becomes t + dt we
have,

Q:^F(i4-<?0 = f(O + F'(i) dt
and

According to the second principle,

Q :

bodies; hence,

^ is independent of the nature of the

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Now, suppose w— y„ becomes indefinite-
ly small and equal to dv; Q'will become
rfQ, Q being the heat necessary to keep
at t the temperature of a body whose
volume increases by dv; hence the dif-
ferential equation of the first order,

(It

(18)

is the differential equation of the second
principle.*

Calculation of the function $ (t). It
may have several forms. Making dt=o
in eq. (0), we get,

\dvl ,

Placing this value of dp in e

'«=«'-.) (I)*-

•See Zeimer, "Thiocie Mechsniqne de
trolBi^eiKCtiOB, 111.
AUo, Cltiiulas OD Heat^ llrst Mcmoif.

, (15),

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Moreovei' in (it) (y-l represents the

partial di

jriv alive

of ;> with

relation

L to (

wlied V h

! constant; making

do—o,

(dp'

'i0

Hence

eq. (18)
.7Q =

ma J' be wt

■itteii,

Equating tliis

with tlie ■

value of rfQ

above, we have,

i*W = (.~.)(|)(|), (..)

from which €• (() may "be calculated.

Again, if we take Eq, (16) and sup-
poeo it applied to bodies whose specific
heats c and <;, are independent, the first
of the pressure and the second of the
volume, as is the case in permanent

gases, these conditions give 1-^1 and
{-j'f equal to zero, and the equation bo-

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(^ '^i'\ /7«^ii

\ dpdu fJ

Dividing eq. (19) by this «

(dl\(dt\
\dhl\di)

(21)

dp do
giving ^ (() as a function of t [=/
(p, v)~\ and of its partial derivatives,

CHAPTER IV.
The Thermodynamic Equations Ap-
plied TO Permanent Gases.
I.

DETERMINATION OF THE SPECIFIC HEAT AT
CONSTANT VOLUME.

Forming, from eq. (3), the partial dif-
ferentials :

(^\~Z {'^\-E _^-L

\dpf'^R'\di!/lVdp.dv B

and a
have

\dp^ R'Vrfij/ IVdp.dv li'
jbstitnting in eqa. (20) and (21), we

(22)

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and ^(()=^^ =(« + ;)■ (23)

,-,-,, . , 1 „ 96.0376

= .160
which is the specific heiit at constant vol-
ume for atmospheric air.

II.

INTEKNAL HEAT.

Placing eqs. (12) and (15) equal to
each other and substituting tlie value of
c from (22), we have :

\dpl

according to eq. (11).

Integrating, and substituting for R its

U=c'r-L7,
or U-U,=c'7- (24)

which shows that the internal heat for
every degree of temperature is increased
by a quantity c' (.16!)), and the increase

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d(i= - ""f -^■J™ , (25)

of the internal heat of a gaa passing from
O^C. to l°G. is always the same, what-
ever variations its pressure may have un-
dergone in this passage, the volume
having been kept constant.

III.

QUANTITY OF HEAT SUPPLIED.

The partial differentials formed from
eq. (3) placed in (15) gives :
■I-Cj0(?a
Tt ■-

which is integrable only when we have a
given relation between p and v.

1. At constant vohime; make do=0,
V being constant. Then

(25a)
which defines the specific heat at con-
stant volume.

2. At constant pressure; here dp=o,
and eq. (25) gives :

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EXPANSION AT A. CONSTANT TEMPERATURE,

To find tlie work done by a gas ex-
panding uothej'maUy, (that is, the abao-
lute temperature is maintained at a con-
stant value), we must satisfy Boylo'e
law and write ;

^iy;^jt)^7)j=constant;
hence pdv-\-vdp=o; or, vdp——pdv.
Substituting this in (25),
,„ {c-c')pdo 1

'—=:jpdv;

Introducing 2> from oq. (y),
and,

q=jE(<, + o/^_^: = 1k(« + i) log. I-

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W=^„«„ log.* — . (26a.)

the ordinary form for peraianptit gases.

EXPANSION IN A PEEFECTTLY NON- CON-
DC CTING CrLINDEB.

If a gas expacii adiabatically, {i.e.,
without any passage of heat either into
the gas from without or out of the gas
into other substances), f?Q=o in eq. (25),
and we have,

c'vdp 4- C2?dv = o.
Writing for — , Its value ;', and integrat-
ing, we have

" di> , p , V

r.P

l<.g.i = log. j--X(-K)=log.^.

rhe logarlihnis, it la seen, sro taken In tie Naperian

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hence, 'fV'' =^J„w/ —tonsiaiit; (27)

an equation which expresses tlic varia-
tion of pressure as a function of volume
when the expansion or compression is
adiabatic.

The external work perfonued during
a finite expansion is denoted by

W= / pih-=J p^vj ——

Since no heat is received from without,
the thermal equivalent of the work must
be estimated as internal heat. If, now,
r„ and r are the initial and final abso-
lute temperatures, the decrease in in-
ternal heat will be

Hence we must liavo,

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Eq. (27) gives i^— j- = l ; multiplying
both members by —jz.j we have,

-£L=(H.)'-'=!f±i=i. (,„)

"' p.

.and

hence,

(r=(i

^)t

_a + t _ T

(31)

SuhatitutiDg i

„(28)

the values of

i".".

from (3) and (^

)'-'

from (;il), w£

> ob-

tain :

R(a + ,

=)|.

-©rf

(32)

r-1

a form often used X^

-=.2908.

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AKIATIONS 1,V THB TEMPERATUKE OF A
GAS DURING BXPASaiOJi OK COM-
PKBSSIOS IN A PKRFECTLT SON-

Plaoing the seooud members of p,v^'=
li (« + *»). >'=^-„ and J=''Ti- i'leq. (29)
we get :

'.-'='{>-(-;)'"'(, (33)

which is thus iiiterpreleit :

The decrease in temperature (duriog
an expansion from w, to v) isprc^ortional
to the initial absolute temperature.

The already esiablished ruiation,

i final temperature as a
funulionof the volumes; and if we know
the initial and final pressures, the final
temperature is exprefised as a function of
these pressures as follows :

a + t T ( i" jy-1

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CHAPTEK V.

Thkbsiodynamic Laws Applied to the
Action of Compressed Air.*

PUNDAMESTAL FORMULAS.

Tile four equations formulating the
law for the expansion and compre.ssion
of dry ail', are, as we have establislied
them,

. ^=R»=e=J(c-»')» (S4a)

(34<J)

• The snbject of tbla chapter Is very ably treaMd by M.
[silard, iu Ibe " Balledb de la Socictc de 1' induetrie

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T}ie.s»? expressions sum up Uie i-elations
existing between the ^ves$ure, volume
anil absolute temperature of a weight of
air tc compressed or expanded in a per-
fectly no n- conducting cylinder.

p„ r„, and v„ have reference to the
initial state of the weight of air consid-
ered, p, T and V corresponding to the
lina! state.

Tlie following table is that of MM.
Mallard and Pemolet. It gives for con-
venient values of — the corresponding
values of — , &c. The tabular differ-
ences faeilitiite interpolation.

{See TiiM.: oit jxtge-i 72 ancf 7:1.)

The coniprussing-cyhnder being sup-
posed perfectly non-conducting as to
heat, our machine may be called a
"Reversible Engine;" for by reversing
the process of compression under exact-

ly GoOglc

,ly the same conditions, we get back the
exact amount of work spent in the c

e com-

The net work necessary to compress a
weight of air w, taken from a reservoir
{as the atmosphere) in which the press-
ure /)„ is kept constant, and to force it
into another reservoir in which the press-
ure is constantly p„ is made u^ of the
following parts: —

1. The work of compression:

2. Diminished by the work due to the
pressure j\ of the first reservoir (the
atmosphere) ; this work is p^ v^, v, being
the volume of weight w ander pressure
/>„ and at the temperature („:

3. Increased by the work necessary to
force the compressed air into the receiv-
ing reservoir; this is given by the
expression p, v„ v, being the volume of
a weight of air w at the pressure p, and
temperature (,.

As no heat passes between the air and
externa! bodies, the thermal equivalent
of the work, according to the mechanical
theory of heat, is the difference between

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T„

■^"

Num-

Differ-

Num-

Differ-

Num-

bers.

ences.;

bers.

ences.

bers,

1,3

i.on43

481

.9486

415

0515

1.4

1.1034

436

.9070

344

0930

l.S

1.1416

439

.8763

393

1374

1.8

1.1850

387

.8433

254

1567

1.3336

343

.8179

333

1831

3.2

1.3569

331

.7056

198

2044

3.4

1.3890

303

.7758

178

3343

S.6

1.3193

187 1

.7580

161

3430

a.8

1.3480

373

.7419

147

3581

1 .3T53

380

.7373

134

3728

3.3

1.4013

348

.7138

126

3862

S.4

1.4360

388

.7018

116

3987

3.6

1.4498

3:i0

.6897

107

3103

3.8

1 .4738

330

.0790

100

8210

1.4948

313

.8690

3310

4.3

1.5181

306

.6598

3404

4,4

l.fi367

200

,6507

3493

4.6

1.5B67

193

.6434

3576

4.8

l.fl760

188

.6345

3655

1.5048

865

.6370

333

8730

1.6813

769

.,i948

360

4053

1.7583

694

.5684

317

4512

1.8376

,5471

183

4530

1.8713

688

.5388

159

4712

1.9SO0

544

,5138

141

4871

3.0044

513

134

5013

2.0556

484

,4864

111

5136

2.1040

457

.4753

101

6247

3.1497

434

,4653

5348

2.1031

.4560

5440

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Table I. — Continued.

Num-

Difier-

Num-

Differ- Num-

Differ-

bers.

eTices.
1317 '

bers.
.8786

ences,
911

793

ences,

1.1382

1.2699

1363 '

,7875

713

695

1.8981

1318 ;

.7163

575

643

1.5179

1179 :

.6588

475

603

1.6358

1145 1

.6113

400 .

571

1.750S

1116

.5713

342 '

546

1.8619

1088

.5371

397 !

534

1 .9707

10155 !

,5074

360 !

505

2.0773

1043

.4814

330 1

488

3.1815

1033

.4684

305 i

473

3.2838

1005

.4379

185

460

2.0843

587

.41H4

167

448

3.4830

973

.4037

151

438

3.5809

937

.3876

139

438

8.6759

943

.3737

127

4JB

3.7703

930

.3610

117

410

3.8633

118

.34B3

111

403

3.9550

006

101

3S5

3.0456

896

388

g.l852

4333

.31S0

3.5685

413S

.3802

390

855

8.9814

3858

.3513

237

334

4.3773

8817

184

317

4.7589

3697

.3101

151

303

3.1386

8583

.1950

126

201

5.4869

3484

,1834

111

281

8430 1

.1713

373

6.1783

334 i

,1618

363

6.5133

8373 1

.153.1

356

6.8396

.1463

250

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the quantity of internal heat }
by the air at its entrance into the cylin-
der, and that possessed by it its exit.

The heat possessed by the air at its
entrance into the cylinder is,

The internal heat at its exit is,

Hence the work of compression is,

and the net work is,

Substituting for p^v^ and p,i\ their
values from eq. (34«) we have,

W,=J«Tc(r,-T„) (35)

an equation perfectly general for dry
atmospheric air.

III.

WORK OBTAINABLE FKOM T[1E COMPRBSSED

If, by any process, we cause a weight
of air 10 to pass from one reservoir, in
which there is a constant pressure p,,

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into another reservoir, in which there is
a constant pressure ^„ and thereby con-
sume an amount of work W^, the same
weight of air w (supposing the air to
remain in the same physical conditions)
will restore the amount of consumed
work W, in passing back from the
second reservoir into the first. These
are the conditions of a perfect thermody-
namic engine.

The work theoretically obtainable
from compressed air is therefore, eq. (35),

W,=Jwe(r,-r„) = W„
an equation which shows how important
it is to take into account the initial and
final temperature of the air,

IV.

THE TBEOKY OP COMPRESSION.

1. The Work iiecessary, and the Volume
of the Compressing- Cylinder. -'N^^\ec\\'a^
all dead spaces and resistances, we can
easily calculate, by the aid of our formu-
las and of Table I, the work necessary to
compress to a pressure p^ a weight of air

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w, taken at a pressure p^ and a tempera-
tore r„, as well as tlie volnme to be given
to the ejliiider of tlie compressor to
compress a given weight of air lo per
secoml, the time T' being given in

Our formulas are :
W,=J«;(i(r, — Tj=J?ocrJ^-l i, (35«)

when a final temperature r„ which is not
to be exceeded, is assumed, the value of

-1- being obtained aa a function of —

from Table 1 , or from an adiabatic curve,

when a pressure ;>,, to which we wish to

W,=

(35^)

an equation employed when wc wish to
find W, as a function of the volume u„ of
the ail instead of as h function of its
weight. This etjtiation is obtained by

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77
substituting in eq. (35(T.) the value of r,
from eq. (Ma.), and y for — ,.
From eq. (34a.) we have,

V,=Rio— xT, (36)

an equation for the volume of the cylin-
der which compresses per second a
weight of air w, when the time, T, re-
quired per single stroke of the com-
pressor (or per double stroke when the
compressor is single-acting), is given in
seconds.

2, The Final Temperature of the Com-
presmd Air. — This is found by loolfitig in

Table I. for the values of — opposite

the different values of — . Supposing

the initial temperature r„=293°=20°C.,

we find for the different values of — the

P,
values of t, in degrees of absolute tem-
perature and degrees C, as follows :

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Pinal Temperature

JD Degrees C.

3J8.3

65,3

•i

403. D

1SU.9

437.9

is4.y

407.3

194.3

4i)3.G

219.6

515.1

243.1

535 4

^63.4

554.1

281.1

071.3

398.8

■187.2

H14.2

ooa.3

;!2fl,3

cie.4

34H.4

639.8

sm.s

643.5 !

sm.5

THE THEORY OF TRANSMISSION.

1. JLoss of JPressure due to Trc
sion. — The lose in pressure which results
from cariying compressed air from one
point to another point diBtaiit from the
fii'st, is due,

1.° To the friction between the air and
the conveying pipes;

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2.° To sudden oontraetioTis in the
pipes;

S.° To sharp turns and elbowB.

From experiments made at the Mont
Cenis Tunnel, the loss of pressure from
friction in pipes was formulated thus: —

Ai)=.0093e'^, (3^)

where «=the velocity of the air per
second,

;= length of the pipes,
(?— diameter " "

Hence the loss of pressure varies,
directly as the length of pipe ; directly as
the square of the velocity of the air in the
pipe; inversely as the diameter of the
pipe.

If w be the weight of air required
by the working- cylinder per second,

3.1416 —u being the volume of air passing

through the pipe per second, and p^ and
Xj being the pressure and absolute tem-
perature respectively of the air in the
reservoir, we have, from eq. {3ia)

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3.1416— f//>,

-i_^j^c-.0;

Solving with respect to u and siibslitu-
ting in (37), we have,

A»=13.S8— i-V.

when Joule's equivalent is taken in
French units ; when taken in IVitish
units (7T!2 foot-pounds per British ther-
mal unit), we have,

Ap=i3.<:\55^'^-^-J (38)

which expresses the loss of pressure due
to friction in the pipes as a function of
the weight of air supplied per second, of
the temperature and pressure of the air
in the reservoir, and of the length and
diameter of the pipe.

2. Difference of iewei.— The difference
of level whieh exists between the reser-
voir and the ctinipressor and the com-
pressedair togine (a-- when the latter is
at the hotlora of a mine) compensates in
part, at least, for the loss of pressure due

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to the friction in the supply-pipes. The
gain in presanre due to this difference of
level is readily calculated by means of
the ordinary barometric formulae. (See
"Wood's Elementary Mechanics, p. 337).

THE THEOKY OF COMPLETE- EXPANSIVE
WOEKING.

1. dotation. — Let 0^=ihe absolute
temperatore of the compressed air when
it enters the working cylinder;

9,=the absolute temperature of the
air after expansion;

^,=the pressure of the compressed air
on entering the working-cylinder ;

^,=the presenre at the e»d of ex-
pansion.

2. Work theoretically obtainable. —
This is given in Section III, and is :

yv,=3wc[o-e;)=3wcd\ i-^'|
=iwce\i-{^'p-\, (39)

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tlie final tempcratiirt'.

^. Final Teniperutim:. — This is given
by e,j. {Md) and is :

it can h<i calculated directly by the use
of Tablo I wlicn wo know -^, the ratio
of tho final to the initial temperature.

4. Volume of the Wor/dnff- Cylinder.
— The volume of the working-cylinder,
being the same ns tho final volume of the
air after expansion is, from eq. (34c(),

v.=-i«'| ('-'■') ■>' <*»■)

wh'ei'e w=tlie weight of air furnished per
second and T=the time in seconds of
one stroke.

5. Weight of Air required pet- Second,
This is determined by the work which is

. to be done by the compressed-air engine
per second. Letting /.■ be a certain co-
efficient embracing resistances of all
kinds, we have, Section III,

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(41)

"~t J(!(e.-e,)

Substituting this valtie of w in eq. (36)
we liave,

R W,T r._ ,/-!

'"Jc'* t («.-«,) '^ft" ^ ^
W T r

the volume of the compressor in order to
supply the given amount of air.

0. Cold resulting from Expansion. —
While in the compressor there is a great
development of heat from the compres-
sion of air, in the working-cylinder there
is a great fall of temperature due to its
expansion. The final temperature 0, is
calculated from the formula of Sec. VI, 3.

e ^

The valves of ^', corresponding to -^,

and the reciprocals, are found from
Table I. The following tahle is from M.
Mallard. The initial absolute tempera-
= 293°, that is, 20° C.

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Pinal Temperature.

Absolute 0,.

1 Degrees C.

; 339 6

! — 3a. 4

313^0

i — 60.0

196.0

i — 77.0

183,7

— 89.3

174.2

166.6

1 -ioe.4

160.3

1 —113.7

154.9

i -118.1

150,1

! -132.9

146.1

; —126.9

: 142.5

-130.5

' 139.3

-133.8

136.3

-136.7

133.6

, -139,4

This table showa what very low tem-
peraturea are reached when we work full
expansion with air at a high pressure.
Ice is formed from the water-vapor
present in the air, and seriously interferes
with the action of the working engine.

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' FULL PRESSURE WOKK-

1. fVork obtainabk. — This is, in the
present case, expressed by the equation,

W,=V,(<5,-#,}. (43)

Placing in this equation the value of V,
from eq. (40) we have,

W, = J„(o-c')e.|l-|l[. (44)

The general expression for the work
restored has been given by eq. (;
' where B, is the temperature of the
after it has been exhausted and has as-
sumed the pressure of the atmosphere

2. Final Temperature. — Placing .
(44) and (39) equal to each other,

"-?'(•

f,\

3. Weight of Air
out?.— This is given by eq. (41).

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4. Vobtnie of Cylinder. — Substituting
w, eq. (41), in eq. (34«), we have,
c-e' W„ T

Jl-
VIII.

WOKlilNi

(46)

EXPANSIVE

1, Work aUainahle. — This is given by
eq. (39).

2, Fitud Teiiiperndire.—'^ c )iave, eq,
(34d),

from which we get 0^' (the temperature
at the end of the stroke). 0^ is then
found from the equation,

(^, _ 1 y—l <P^

3, Ihe weight of air used. — This ia
given by eq. (41.)

4, Volume of the Cylinder. — Eq. (34«),
written to satisfy otir conditions, be-

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V,=J(»-c')»T|i,

■, substituting the value of w from eq.
1).

-, _ y-l W,T

$■:

(47)

IX.

GRAPHICAL REPEESKJiTATION FOE THE
ACTION OF COMPBKSSEn AIR.

Let abscissas, in diagram on next page,*
be volumes, and ordinates pressures;
taking for the origin. Through B
{Pt^t) construct an adiabatic curve from
its equation, (eq. 2V).

"The intrinsic energy of a fluid is the
energy which it is capable of exerting
against a piston in changing from a given
state as to temperature and volume, to a
total privation of heat and indefinite ex-
pansion." The intrinsic of 1 lb. of air
at p, and v„ will be represented by the
area included between the axis of

• For which we are Indebted to PnrfeBsor Frailer.

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abscissas, the ordinate AB=jo, (at a
distance from the origin OA=v„), and
the portion of the adiabatic curve ex-
tending indefinitely from B until it be-
comcB tangent to the axis of abscisBaB
when a;=oo. The algebraic expression
for this area {found by integrating eq.
(27 a) between the limits =0 and w, is,

1=^. (48a)

^,=mean pressure of atmosphere in
lbs. per square foot=2n6.3;

ii^=volume in cubic feet of 1 lb. of air
at pressure^, and temperature T,
= 12.387;

T,=493,''2 corresponding to 32° F;

^= 1.408 ; hence

1=^°-°- =64250 foot-pounda;

that is, one pound of air, at mean baro-
meter pressure and 32°F, possesses an
intrinsic energy of 64250 foot-pounds;
and il is up<y>i this store of energy that
vie draw, when, after abstracting in the
form of heat all the work we had ex-

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in compressing the air, we yet
cause it to perform, work by expansion.

Through B constnict an isothermal
curve fvotn its equation (eq, 1), At a
point (as ]^) chosen arbitrarily upon
this curve to correspond to a desired
pressure we can construct anotlier adia-
batio curve LliK Then will the rela-
tions exist, expressed as follows, and
given by Prof. Frazier :
Area ABOC prolonged indefiniteiy =
intrinsic energy possessed by the
air before compression = I.
Area ABLPA=the work performed in

compressing the air.
Area DBLEN prolonged indefinitely —
ABLPA=energy in the form of
heat abstracted by the cooling
water; consequently, 13SND pro-
longed indefinitely =ASLPA.
Area CKRN prolonged indefiiiitely=
intrinsic energy of the air after
expansion.
Area KKLPK=work performed by
the air in its expansion.

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Area ABRKA— work performed by

the air after it leaves the working- .
cylinder.

AreaDBRSN prolonged indefinitely =
ABRLPA=the heat ahsorbed
by the air after leaving the work-
ing - cylinder.
For iaothernial compression, we have,

Area ABLHOA— total work perform-
ed in the compressing- cylinder.

Area ABLPA=work performed in the
compression of the air.

Area PLHOP=^work performed in the
expnlsion of the air from the corn-
Area ABUOA=work performed by
the atmosphere.

Area UBLHU- ABLPA^the work
performed by the motor.

Area [JTLIIU=useful work performed
by the air (full pressnre).

Area UBLHU - UTLHU = TLBT=
amount of work lost.
For adiabatic compression we have :

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Area ABXYA = work performed in
the compression of the air.

Area TXHOY=woik performed in
the expulsion of the air from the
compressor.

Area ABUOA=work performed by
th# atmosphere.

Area BXHD"B=work performed by
the motor.

Area TLHUT=usefnl work performed
by tije air (full pre&sure).

Area BXLTB=BXHUB-TLIIUT=
amount of work lost.

When the air is allowed to expand
fully (to its original pressure joj,

Area KTLR=H8eful work of ex-
pansion.

Area UHLRU=total useful work (=
UTLHU + ETLR}.

Area BXLRB= BXHUB- UHLRU
--amount of work lost where air
is cooled after leaving the com-
pressor.

Area BLRB = UBLHU- UHLRU =
amount of work lost where air is
eooled completely in compressor.

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The area BLRB represents, then, the
excess of work performed on the air
above that performed by it, or the
amount of work permanently transform-
ed into heat. It is, therefore, not possi-
ble, even by preventing any rise of tem-
perature during compression and allow-
ing the air to expand to its full extent,
to obtain from the compressed air as
much work as was expended in the com-
pression. We can obtain from com-
pres^ed air all the work expended upon
it, only by causing it lo reproduce exact-
ly during its expansion the changes of
condition it underwent during compres-
sion. This may theoretically be accom-
plished in three ways.

1. By allowing the compressed air to
become heated during compression, and
preventing all transmission of heat until
it leaves the working cylinder. It will
be compressed and will expand in this
case following the curve EX.

2. By cooling the air during compres-
sion and heating it during its expansion,
in such a manner that its temperature

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shall remain constant during both opera-
tions. The air will be compressed and
will expand in this case, following the
curve BL. The heat abstracted during
compression will equal that su]) plied
during expansion.

3. By cooling the air before its com-
pression to such a degree that after it is
compressed it will have the temperature
of the media surrounding the working
cylinder. ■ The air will be compressed
and will expand in this case, following
the curve RL.

CHAPTER VI.

Efficiency Thkobetically An

EFFICIENCY Of THE A
COMPEESSEU-AIK ENGINE AS

Work performed on the air_
Work performed by the air

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w._ jc(e.-e,)i»

"W,~Jc(r,-r,)«i

isi--

Tnpraotice, ^aiid — differ very Uttle

in value, their difference being due to
the losa of pressure frum the friction be-
tween the air and the supply-pipe, a loss
which is very small if the pipes are of
sufficient diameter.
Hence we may write,

that is to say, when compressed air is
made to expand completely, and when
the ratio of its pressure to the pressure
of the surrounding atmosphere is the
same when the air leaves the compressor
as when it enters the cylinder of the
compressed -air engine, the efficiency of

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the system is the ratio of the temperature
of the compressed air when it leaves the
compressed-air-engine cylinder to the tem-
perature of the air at its entrance into
the compressor.

This law ia indepeiideot of any heat
lost by the air in passing from one cylin-
der to the other.

Since we have just admitted that,
1^1 _;>,

showing that the loss of work is propor-
tional to the loss of heat undergone by
the compressed air in its passage from
the compressor to the working-cylinder.

The efficiency will be a maximum
when r,=0, ; that is, when the loss of
heat is nothing. Of course, this con-
dition cannot be realized. Generally the

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r reaches the working
cylinder with a temperature equal to
that of the surrounding atmosphere.
The temperature 0, is therefore given,
and the etfieiency can only be increased
by diminishing r^.

The following table is calculated from

(eq. 48fi) for different values of — , the

^ P.

temperature of the compressed air at
entering the working cylinder being
taken 9^=29Z°, that is, V0° C.

The table shows that when the press-
ire has reached four atmospheres, even

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a considerable increase of it does not
much effect the efficiency.

MAXIMUM EFFICIENCY CALCULATED FKOM
THE IXniCATF.J) WORK.

Let p— the pressure of the compressed
air,

Let^„=the pressure of the atmosphere,

V and i/^=ihe corresponding volumes;
also let f=fip^ ,• then v=hz\.

The work spent upon the air to com-
press it, is, {e<j. 20«),

W|=;)^!; nap, log, =p^»x

2. sort com. log. ?i
The work performed by the air is :

and as^!'^=j)^y and v = nv^, we have

w,-?.»|i--[;

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3 com. log. n (^^■)
Sabatitating different values of n in
this formula we get the corresponding
values of E.

THE EFFICIENCY OF COMPLETE EXPANSION
AND OF FULL PEESSUKE COJIPAKED.

To show tbe comparative merits and
demerits of full pressure and complete
expansion in the use of compressed air,
we present a table prepared by M. Mal-
lard:

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1^"

■tm

SjS E'S

I ! I M I I I I I I I I I

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The initial temperature Is assumed at
20''C.

The table shows that by working non-
eipansively we avoid very low tempera-
tures of exhaust; but this ia of little
practical importance when we take into
account the low efficiency of full pressure,
as compared with complete expansive
working. Also when working at full
pressure, the higher the working pressure
the lower the efficiency.

CHAPTER VII.

The Efpbcts of Moistueb, op thk
Injection op Water, and op

THE CoHDUCnON OF HkAT.

GENERAL STATEMENT.

In dealing with compressed air we
must always keep in view the very im-
portant consideration of the initial and
iinal temperature of the air.

There are two principal causes tending

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to vary the amount of heat present in
the compressor or abs^orljed in tlie work-
ing-cylinder: —

1. Tlie water or water-vapor of which
atmospheric air always contains more or
less, and which is purposely introduced
into the cylinder of the so-called wet-
oom pressors.

2. Tlie conduction of heat by the
cylindei's, supply-pipes,

THE liFFECTd 01'' MOlaTUHE.

Atmospheric air always contains more
or less moistare. Wo wisii to consider
the effects of this moisture upon the air
undergoing com]iresBion or expansion^
The injection of water into the cylinders
and its cooling or heating effects arc left
out of the question altogether, as they
will receive attention further on.

In all conditions of temperatui-e and
pressure practically realizable, a mixture
of air and saturated water-vapor will
remain saturated when the mixture ex-

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pands against a resiatance, a certain
quantity of water being thereby con-
densed ; on the contrary, compression
superlieats the vapor, which tlieii
becomes n on -saturated, and non-satu-
rated vapors follow the laws of perma-
nent gases.

1. Infiuenise of wuter-vapoi- upon tlie
work spent on the air and upon that
performed by It. — The presence of mois-
ture in the air has been found to be
favorable both in the compressor-cylin-
der and in the working cylinder. In both
cases, however, the gain in work spent
or performed is so slight that it can be
entirely neglected, and the formulae
already established for dry air become
applicable with a sufficiently close
approximation. In the case of com-
pression, the vapor is superheated and
therefore comports itself very much like
the air itself; while in the working-cyl-
inder, the increase of work performed,
when the initial temperature of the
compressed air does not exceed 30° C,
is very small; and, as the temperature at

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104

which compressed air is used, is rarely
higher than 20° C, the influence of the
water-vapor can be safely neglected.

2. Itifluence of the moislure of l/ie air
upon the Mnal Temperature. — The pres-
ence of the moisture in the atmospheric
air introduced into the compreasor tends
to lessen the heat of compression; this
effect, however, is very slight, and, in a
practical point of view, is not worth
considering.

When compressed air is completely
expanded in a working-cylinder, the
presence of moistare in it tends to lessen
the cold produced. M. MallaM has
found what the initial pressure would he
for certain initial temperatures, so that
the tinal temperature should not fall
beiow 0° C. He has found this for hoth
dry and saturated air, and his results are
tabulated as follows: —

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Pinal tern-
peralure.
Degrees C.

Initial tem-
Hiraturc.
Degrees C.

i6
Value of — ° wltli tlie

air.

Saiurated 1
wilh water- Dry.
vapor. 1

0°
0°

20^
30°
40"
50°

l.rO 1.376
1.89 1 1 433
3.39 l.(i03
3.06 1-780

This table shows that,
air at 50°C and at a pvessuie of three
atmosjilieres be introduoed into a work-
ing-cylinder, this air, if saturated with
aqueous vapor, can bo completely ex-
panded without falling to a temperature
beliiw 0°C; and that this air, if dry, dare
not exceed an initial preesore of 1.78
atmospheres if its tinal temperature is
not to fall below 0°C.

3. Volume of Che Ci/linfters. — '1 his is
calculated as for dry air, since the effect
of tlie m,.isture is too slight to be taken
into aeeount.

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THE INJECTION OF WATEU.

I. Ilia Effect- of Introducing Water
into the Compressor- Cylinder. — It is of
great advantage bi practice to intro-
duce cold water into tlie compressor.
It carries away the heat of compression
to a very great extent. It acts as a lu-
bricant, and, by cooling the cylinder, it
prevents the destruction of any organic
material, such as packing, valves, &c.,
that may be employed upon it.

If in addition to the atmospheric
moisture present in the air at its entrance
into the compressor, water be introduced
in quantities juat sufficient to keep the
air saturated with water-vapor during
the compression, the work spent upon
the air and the final temperature at the
end of compression will both be less than
if the air had not been kept saturated
while being compressed. It is unneces-
sary to calculate the amount of work
saved or the extent to which the tem-
perature is reduced by the presence of

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this saturated water-vapor; for if water
is at all to be introduced into the com-
pressor, it may as well be thrown in in
larger quantities, that is, in quantities
sufficient to absorb and carry off the
greater part of the heat of compression.

The effects of the heated air in the
compressor is a great cause of loss of
motive power, and it is very desirable to
cool the air during its compression.

The final temperatures for different
pressures have already been given in
Table II, We repeat them here in con-
nection with the quantities of work
spent when the compression follows
Boyle's law and when it is effected with-
out any removal of heat.

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ZiS.'lS

gsss^ss

E-S bS

Iiig§i

Siiliii

J ^

■s

fi=

ggSfSSS

■efebs

ojcot-eSmoio

o o a)

(-"» t-'-H';*!-'^

1 .

^ss

■-„£

MOfo-rrxs,

I'll

SSmmStSS

J ^

o"S

a^iiiiii

r-i,

~«s

CvaSCOinOOW

■^&s

— *S S! lO ^ O 'P

2 "

lis

-"23SSSS"

Is !S

3 g2

ggiilSss

_ s

;2.ss

noiBuaj,

"°"°"°""" 1

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109

The Quantity of Water to be Injected.
—We have found eq. (26), that the
quantity of heat developed by compres-
sion 18 given by the formula,

Q= -^'nap. 'og,|^"[,

where r, is the absolute final temperature
= 273°-|-40°=313°. From this formula
the quantity of heat, Q, is calculated for
different pressures. We then find the
weight of water, whiob, if introduced at
20°C and removed when it has taken up
enoQgh heat to raise its temperature to
40°C, would absorb this quantity of heat
Q. Under these conditions we find that
each kilogramme of water will absorb 20
calories. Dividing Q by 20 we get the
weight of water to be introduced in
kilogrammes. In (his way the follow-
ing table was prepared :

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Weiglit of water at

Heal devel-

20° C. to be injected

Absolute

oped hycom-

into the compreBSor

pressure to

preasion and

per kilogramme of

which the

to be carried

air compressed in

air is com-

off by the

order to keep the

pressed.

injected
water.

flna5 temperature

from rising above

40° a

tmosplieres.

calorics.

kilogrammes.

14.695

.794

2'i.28i

1.164

39.392

1.469

34.120

1.701

S7.979

1 891

41 .864

3.063

44.087

3.304

46.589

48.816

2^440

50.849

3.543

52.694

2,634

54.391

3 719

5S.962

3,798

57,425

2.871

2. 77ie Injection of Hot Water into
the Cylinder of the Compressed-Air
Engine. — In tlie production of compress-
ed air, tlie great cause of lose of motive
power, as we have seen, is the develop-
ment of lieat. Analogous to this is the

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loss which occurs in the use of compress-
ed air. Great cold is produced by
expansive working, and this has long
forbidden its adoption. The injection
of hot water into the worliing-cylinder,
has now made it possible to attain the
desirable result of working expansively.
The Quantity of Hot Water to be
Introduced. — The quantity of heat, Q, to
be supplied to keep the temperature of
the expanding air constant is found from
eq.(26), to be,

Q=y'nap. log.jM.

The expansion being supposed to follow
Boyle's law, we have,

Hence we have,

Q=?Iv.p.,„,.|&f.

^,=1 in this case since the air is expand-
ed down to atmospheric pressure. I'rom
this formula the weight of water to be
injected is calculated as in table. The
results are given in the following:

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Weight of water lo be injected into the work-
ing cylinder per kilogramme of compressed
air introduced to Itecp the final temperature
from falling below 0° C.

1?
1"

2 =>

— in

gSSSIii^gliSii

—

Quantily of heat to
be supplied to keep
the temperature of
the air from falling
below 0° C. during
its expansion down
to atmospheric
preaaure.

iMpiiipsS|l

If.

1 1'%-

.„„,=.«, 3-2333

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The quantitieB of water here given are
the minima values, einee the ktent lieat
whiuh is released by the water in fieezing
has not been taken into account. Ilence
to avoid the formation of ice we must
add a slight excess of hot water.

3. The Effect of the OomJuction of
Heat by the Cylinders, Pipes, &c. — Since
the temperature, of the compressed
air when ttsed is most alwiiys that
of th^ surrounding atmos|>l)ere, tlie
result of the conduction of hewt by the
containing vessels is the dissiijaiion of
the total heat of compression. The me-
chanical equivalent of this heat is, of
course, lost work, and, as it is most
economie;il to get vid of this tieat during
eompresiiion, conduction and r;idiation
from the compressor is an advantage.
Since, in working expansively, there is a
tendency for the cylinder to become
colder than surrounding bodies, the con-
duction and radiation of heat is here too,
if anything, an advantage.

In all our formulas and results hitherto
established, the cylinder have been sup-

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posed noii-coinluotiiig; and the iuvesti-
gations of M. Mallard have sIiow^d that
this hypothesis ia justified. For the heat
leaving the compressor by conduction
and radiation is in part compensated for
by that developed by the friction of the
piston; and the heat conducted through
the working cylinder ia very small rela-
tively to that converted into work.
Hence, any passage of heat by conduc-
tion of the cylinders belongs to those
secondary quantities wliich are always
omitted in the general theory of motors,
except so far as allowed for by proper
coefficients.

CHAPTER VIII.

American and EuitorsAS Aik-Com-

rUMP COMPRESSORS.

Pump or plunger compreasora are
generally in high repute in Germany and
Austria, especially in mines, and they

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seem to give very satisfactory results.
In the United States they never have
been used to any considerable extent and
are now not at all used.

It must be said to the prejudice of
these compressors, that, iti consequence
of the large mass of water to he pushed
hack and forth by the plunger, a large
per-centum of power is wasted in over-
coming inertia; that high piston speeds
are, in consequence of the violent shocks
which result, utterly impossible; that
they are very heavy and hence require
expensive foundations; that when the
prime mover is run at a high speed, a
more or less cumbrous, expensive, and
wasteful machinery of transmission is
necessary ; that their nse ia limited, press-
ures of 6 or 6 atmospheres being their
utmost capability, on account of the
large quantity of eooliog water taken up
by the air at even moderately high ten-
sions; that a large amount of cooling-
water is required to produce a compara-
tively small effect in the abstraction of

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On the other hand, k must be ad-
mitted tliat these compressors are liable
to very fnw repaii's, that they ai'e simple
ill uoiist ruction and that "defld s|>ace8"
are avoi<led.

The hydraulit! or ram eoni|irossor8
first nsed by Sommeiller at llie Mt.
Cenis Tiiuntl have beeomo obsolete.

<;LH-4CriNG WET COMPKES&OKS.
ed i

the

Tlic ail- compressors n
UniLed States are either, Drt) Compress-
ors ill wliieh the eoolini; is effeili'd by
floodinsf the external of the cylinder, and
aometirries also the piston and pision-head
with water; Wat Compressors, by the in-
jeoti'iii of water into the eyliniler-spaee,
aa Weil as by external flooding ; compress-
on with no cooling arrangement are
seldom (i-ed, and only in tempoiiiry and
cheap plants.

Comi'ressors with a partial injeetion
of wilier have been used to verv good
effeet in the United States. Mi>st of

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Ill

these are single-acting, and are repre-
sented by tbe machineB of Burleigh, of
Fitcliburgli, Mass. The cooling is very
efficient and hence the useful effect is
considerably increased. They are very
durable and not liable to get out of re-
pair, as is shown by the record of Bur-
leigh's machines, which have stood the
test of years of steady work.

The use of single-acting compressors
renders it necessary that, in all cases
where anything like a uniform supply of
air is needed, to have two compressor-
cylinders. These cannot be driven
directly from the piston-rod of the
driving engine, bnt necessitate an in-
directly coupled-connection of some sort.
Alt this makes single-acting compressors
somewhat cumbrous and expensive.

As built to-day, the evils of dead
spaces, and of jars and shocks resulting
from water in the cylinder, have not been
duly considered. There are also a few
cases when the sectional area of the
inlet-valves is insufficient; and in gener-
al those parts which are most liable to get
out of repair are most difficult of access.

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11*

We iire inclined to think that tlie
claim of the Burleigh Co., that tlieir
compressor is the most oflicieiit, economi-
cal, and durable of any huilt in thit;
coiintiv cannot be far from the truth.

DOUBLE AND DIRECT-ACTING

Up to within several years ago, single-
acting compressors Lave been used
almost exclusively. Now the double
and direct-acting compressor seems to
be superseding it. This is now the
leading type of American compressor,
although hitherto it has given at least no
better results than the best single-acting
m.aGhitie.

Superiority in tlte double-acting com-
pressor is found in its simplicity. The
piston of the engine drives the compress-
or by a direct connection. All wasteful
and cumbrous machinery of transmission
is at once unnecessary and high piston-
speeds are possible; in the United States
from five to seven feet.

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Most American double and direct-act-
ing conipressora are of the dry kind.
These have the advantage that the air ie
delivered without having any water
mechanically mixed with it. Hence
very much ice cannot be formed when
the air is worked expansively. Higher
rates of expansion are possible than with
air from a wet compressor.

One of the very best American double
and direct-acting dry compressors is the
"National," built by Allison & Brannan,
Port Carbon, Pa., (Office, 95 Liberty St.,
N. Y.). Steam cylinders of the medium-
sized duplex machine are 12'X't2°, and
the air cylinders 15'x42''. The air
pistons work to within one sixteenth of
an inch of the cylinder heads. The
water circulation ■ for cooling passes
spirally around the air cylinder from the
center to each end. The engine will
compress air to the same pressure as that
of the steam used. The amount of free
air compressed at a piston speed of 350
feet is about 1000 cubic feet per minute.
A greater pressure of air than the press-

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lire of steam used is obtained by iiicieas-
ing the size of the ateam cylinder, or
decreasing that of tiie air oylinder.

The best double and direct acting
compressor of the wet kind is undoubt-
edly that of Dubois- Fran fiois, built in
Seraing, Belgium, and exhibited at the
Centennial Exposition, in ia~6.

Dry compressors, although the cheap-
est as regards first cost, are not the most
economical in working. But where air
la to bo carried through pipes exposed to
great cold they are the only alternative.

IV.

DESIGN AND CONSTRUCTION.

The efforts of builders and engineers
should be directed to the attaining of a
higher efficiency, and they should not, as
is now often the case, sacriSce the latter
to cheapness and small dimensions. To
attain such desirable efficiency the heat
of compression must be more effectually
abstracted. This must be done by a
more ingenious and rapid circulation of

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water around tlie cylinder, and injeo-
tion of water in ihe form of spray into
the cylinder. But the injection of water
•n some efficient and practical manner,
which is fio essential to the i-eaching the
highest efficiency, introduces the great
disadvantage of having to work with
wet air. Hence we see how important
would be an invention of means or ap-
paratus for separatmg the water from
the air when direct intereontact haa
been had to keep down the temperature-
We must also remember the important
physical fact that water absorbs very
considerable volumes of air — volumes
dependent upon the pressure of the dr
and the amount of surface of water ex-
posed to the fluid contact, time being
also an important factor.

Clearance must be reduced to the
smallest possible amount. It has been
brought down in a few cases to 0.39
inch. A long stroke, one from 2 to
to 3 times the diameter of the cylinder,
is another means of avoiding loss from
dead spaces, since here the air which

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fillR the dead space is small in compari-
son with that actually delivered. The
valves must be go placed that, between
their scats and the piston-head at the
end of the stroke there shall he the
flmallest possible clearance.

The valves themselves, to close the
more rapidly, are made to have only a
very small travel. (This has been made
ae small as .OS to .12 inch.) The
valve-area must be made large enough
by increasing the number of the
valves. It should be amply large,
generally from ^ to -jV of the sectional
area of the cylinder. The valves should
he so attached to the cylinder-head that
they may be removed and repaired with-
out taking off the latter or otherwise
taking the machine apart.

Great care must be taken to have the
piston head fit the cylinder accurately
and closely, since, especially in dry com-
pressors, great losses result from any
looseness. The piston-heads should be
made so that they can be adjusted to
preserve a nice fit, as in steam engine

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practice. Lubrication of the cylinder in
case of the dry compressor should be
effected by automatic oil oupa placed
upon it.

It must alao be borne in mind that the
working pressure is that which most
influences the physical conditions of
working, and the suitable mode of con-
struction. And, although the loss of
work increases with the pressure, yet the
rate of variation of the loss of work
decreases as the pressure increases. As
great a proportion of work is lost by
increasing the pressure from two to three
atmospheres as by increasing it from
five to ten atmospheres.

The tendency in Germany and France,
as well as here, is for the wet compressor
entirely to supersede all others. Bat it
is scarcely too much to say that the
air-compressor of the future has yet to
be invented.

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CHAPTER IX.

Examples prou Pk actio e.
I,

The Republic Iron Company of Mar-
quotte, Mich., have done away with the
use of steam, by utilizing the power of .a
water-fall situated about a mile from
their works. The power ia transmitted
by means of compressed air wbieh drives
all their machinery, and thus saves the
cost of fuel.

There are four compressors, 24' diam.-
eter and 5' stroke, driven by two turbine
Swain water-wheels 6^' diameter, under
16 feet head of water. As near as has
been ascertained, they have about 450
horse power at the wheels. The air is
carried one mile in a pipe built of boiler
iron, 15" inside diameter. About 06 per
cent, of the effective power of the wheels
is obtaine<l at the mines and shops.

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ECONOMY PROMOTE I> BT THE D8K OP

To show the great saving of both time
and money since the introduction of
compressed-air machinery we will give a
few fignreB.

It coat the Golden Star Mining Co., of
Sacramento $12 to $15 per foot to run a
tunnel 7x7 feet, wlien employing hand
labor; after introducing air machinery
it cost them $6 to $7 per foot; with
hand labor they made a distance of two
feet per day; with machine labor, a dis-
tance of six feet per day.

Another instance, among many, ia
that of the Sutro Tunnel Company of
Nevada;
Expense by hand labor per

month $34,000 to $50,000

Expense hj machine labor

per niontli $14,000 to $16,000

III.

COMPRESSED- A IK MOTOE STREET CAB.

The pneumatic engine which has been

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126

oil trial by the Second Avenue Railroad
Company, on the Harlem portion of their
road, from the Station at Ninety-Sixth
Street, to Harlem River, at One -Hundred"
and -Thirtieth Street, has proved ao satis-
factory to the company that it has au-
thorized the construction of five more
engines.

These are to be used exclusively on
the upper part of the road, where it is
proposed to dispense entirely with the
use of horse power, so soon as the
requisite number of engines shall be pro-
cured. It was stated at the company's
office, that the most sanguine ex-
pectations had been fulfilled; the new
engine could be run at a trifling cost,
and without the ooiee and smoke and
smell of oil which accompany the use of
steam; any rate of speed which was
likely to be required could be maintain-
ed, and the engine was under as complete
control of the engineer as one propelled
by steam or a car drawn by horses.

The new engines are manufactured by
the Pneumatic Tramway Engine Com-

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12T

p any, whose office is at No. 317 Broad-
way. Some time ago two Scotch engi-
neer, Rohert Hardie and J. James, in-
vented a system of propelling cavs by
means of compressed air. The invention
was examined by a number of practical
railroad men who were visiting Scotland.
Hardie and James were induced to visit
this country and the company was or-
ganized. Experiments have been making
for a year, resulting in improvements
which now seem likely to render the in-
vention serviceable to the public. The
motive power is condensed air, contained
in two reservoirs, placed one under each
end of a car, which is similar in con-
structioti to those in ordinary use on
street railways. The air is pumped in by
a stationary engine at one liundred and
twenty-seventh street, and this has been
so far improved that the reservoirs in
the cars now used are filled in a few
minutes. These are of steel, and are
tested up to a strength many times
greater than their working pressure, and
it is claimed that there is no danger of

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V2B

explosion. The machinery ia simple and
not liable to get out of order. The air-
tanlts of tile cxperiineiital car are only
sufficiently large to enable it to make
one round trip between Harlem and
Ninety-Sixth Street stations ; but the
cars now building will be larger and will
contain reservoirs of nincb greater
capacity ; and it is claimed that there
will be no difficulty in constructing them
so tbat the round trip from Harlem
river to Peck Slip can bo made without
replenishing.

Mr, Henry Bushne!), of New Haven, is
tbe inventor and constructor of anotber
new compressed air motor street car, the
chief peculiarity of wliicb is that he is able,
as he says, to force air into his receivers
until liis gauge registers the enormous
pi-essure of more than 3,000 pounds per
square inch. His receivers are tubes, the
largest of which are twenty feet long, and
only eight inches in diameter, inside meas-
urement. There are four of these, two
lying side by side above the axles, and
next to tbe wheels on eithiT side of the

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129

car. Between them at one end are four
other tubes, each six feet long and six
inches in diameter, inside measurement.
The material is wrought iron three-
eighths of an inch thick, and are welded
in. The double cylinder engine which
tttilizea this air in turning the wheels of
the car does not differ materially from a
Steam engine, except that its two cylin-
ders are only two and three-fourths
inches in diameter, inside measurement.
The machine built by Mr. Bushnell to
compress the air consists of three steam
air pumps. The first and largest is
merely a feeder to the second. The air
that comes from it is condensed to a
pressure of about six pounds. This den-
ser air is more worthy the prowess of
the second pump, which in turn crushes
it into a greatly smaller compass. The
third pump gives the final pressure.
The gauge on the compressing machine
has registered 3,500 pounds per square
inch. The plungers of the second and
third pumps have no heads. They are
merely rods of steel forced into vessels

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containing oil. As the plungers inovc
out and in, the surface of tlie oil falls
and rises, admitting the air through one
valve and forcing it out of another. It
is, tlioj-efore, necessary to have the pack-
ing of the plungers only oil tight, not air
tight, under the tremendous pressure.
The chamber that first receives the air
from the tliird pump is cooled by
a covering of cotton waste saturated
with water. On the other hand, the ex-
pansion of the air as it is given off at
each half revolution of the car engines
absorbs heat, and after i-unning the car
for a short time the engine cylinders and
escape pipes are whitened with frost.
To remedy this Mr. Bushnell will sur-
round the cylinders with stout metal
jackets, beneath which he will force air
with the aid of a small pump geared to
the machinery of the car. This newly-
compressed air, he says, will supply heat
enough to keep the cylinders warm.

The writer rode recently on the new
car as far on the Whitneyville road as
Mr. Bushnell could go without interfer-

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131

ing with the trips of the horse cars. The
motion was easy, and at times about
twice as rapid as that of a horse car.
The new vehicle obeyed the engineer
promptly in starting and stopping. The
distance traveled in going and returning
was a little over a mile. At the start
the guage registered 1,800 pounds. At
the return the pressure indicated was
1,500 pounds. When the air was al-
lowed to escape from a turned cock the
roar was frightful and was as irritating
to the ear as escaping steam. In run-
ning, however, very little noise is heard
from the escape-pipe, because the es-
caping air is made to pass through a
mass of ordinary curled hair. This device
Mr. Bashnell esteems one of the most
important of his inventions. He has no
doubt that It would prove equally effica-
cious in deadening the sound of escaping
steam.

Friends of Mr. Bushnell claim that he
could never make a receiver capable of
retaining air at the high pressure he had
in view. The air that was in the tubes

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132

was pumped in, lie says, on the 25th of
June. The gauge then showed 2,100
pounds. The pressure gradualiy lessened
unlil it was 1,900. After that lime a
snaall leak was diKCOvered. Tbls leak
was dosed wiih a turn of the wrench,
and after that not a pound was lost up
to the trial, when 100 pounds was
allowed to blow off to gratify the curi-
osity of visitors just previous to the
short trip referred to.

Mr. Bushiiell called attention to the
amail diameters of his largest tubes.
He said that a pressure of 2,000 pounds
per square inch would give, by calcula.
tion on the head of each tube, an aggre-
gate pressure of fifty tons; while the
two-feet heads used by the inventor of a
rival compressed air motor would have
to withstand an aggregate pressure of
180 tons, if a pressure of £00 pounds per
square inch should be put on, as the in-
ventor claimed was possible. The heads
were necessarily the weakest parts of the
lubes. A welded joint, such as his were,
was usually reckoned twice as strong as
a riveted one.

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On a previous occasion Mr. Bushnell
made a round trip on hia car on the
Whitney ville road, a distance of a little
over four milefi. The pressure was then
reduced from 1,950 pounda at the start
to 750 pounds on the return. A com-
pany called the United States Motor
Power Company haa been formed, and
Mr. Bushnell is its president.

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